GLASGOW—The U.K. economy is gaining strength but will face persistent headwinds in the years ahead that are likely to keep a lid on future rises in interest rates, the governor of the Bank of England said Wednesday.

In a speech in Glasgow, Scotland, Mark Carney said the U.K. central bank has no "preset course" to determine exactly when to lift its benchmark rate from a historic low of 0.5%, where it has been pegged since...